A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries

Abstract

a b s t r a c tIn this paper we propose a flexible model to describe nonlinearities and long-range dependence in time series dynamics. The new model is a multiple regime smooth transition extension of the Heterogeneous Autoregressive (HAR) model, which is specifically designed to model the behavior of the volatility inherent in financial time series. The model is able to simultaneously approximate long memory behavior, as well as describe sign and size asymmetries. A sequence of tests is developed to determine the number of regimes, and an estimation and testing procedure is presented. Monte Carlo simulations evaluate the finite-sample properties of the proposed tests and estimation procedures. We apply the model to several Dow Jones Industrial Average index stocks using transaction level data from the Trades and Quotes database that covers ten years of data. We find strong support for long memory and both sign and size asymmetries. Furthermore, the new model, when combined with the linear HAR model, is viable and flexible for purposes of forecasting volatility.

Realized Volatility: A Review

“…The HAR-RV model is specified as a multicomponent volatility model with an additive hierarchical structure such that the volatility is specified as a sum of components over different horizons (see also Andersen et al, 2006a). McAleer and Medeiros (2006) extended the HAR-RV model by proposing a flexible multiple regime smooth transition model to capture nonlinearities and long-range dependence in the time series dynamics.…”

It's all about volatility of volatility: Evidence from a two-factor stochastic volatility model

“…Corsi et al (2008) and Corsi (2009) show that the HAR model is able to reproduce the longrange dependence typical of RV series. However, as noted by Maheu and McCurdy (2002) and McAleer and Medeiros (2008), the dynamic pattern of RV is subject to structural breaks and could potentially vary over time. This evidence is also confirmed by Liu and Maheu (2008), Choi et al (2010) and Bordignon and Raggi (2012) who find that structural breaks in the mean are partly responsible for the persistence of RV.…”

“…Primiceri (2005), Cogley and Sargent (2005) and Koop et al (2009) among others, testify the empirical success of such models in characterizing macroeconomic series. In contrast to Liu and Maheu (2008) and McAleer and Medeiros (2008), our model allows for a potentially large number of changing points of the HAR parameters. In particular, we let φ d , φ w and φ m in equation (1) 4 follow random walk dynamics.…”

Modeling tick-by-tick realized correlations

“…To overcome the problem, and also to ensure computational feasibility, we searched for threshold values over fixed grid points that are empirical quantiles of the different predictor variables. Alternatively, McAleer and Medeiros (2008) and Medeiros and Veiga (2009) recently proposed a sequence of tests to determine the number of regimes for a class of smooth transition models for the dynamics of financial (realized) volatility which circumvents the problem of identification in a way that controls the significance level of 6 the tests in the sequence and computes an upper bound to the overall significance level. Such a strategy can be easily adapted to the case of fitting tree-HAR models.…”

“…Similar to the smooth transition heterogenous autoregressive technique proposed by McAleer and Medeiros (2008) which modeled the realized volatility of sixteen US stocks with good forecasting results, we propose a regime-dependent, tree-structured heterogeneous autoregressive (tree-HAR) model for the estimation and prediction of the tick-by-tick realized correlation series. The conditional mean dynamics of the realized correlation series follow local linear HAR processes and are subject to regime shifts depending on past values of certain relevant predictor variables, such as, for example, past returns, past realized volatilities or time.…”